Problem: Express your answer as a mixed number simplified to lowest terms. $9\dfrac{1}{10}+12\dfrac{5}{15} = {?}$
Separate the whole numbers from the fractional parts: $= {9} + {\dfrac{1}{10}} + {12} + {\dfrac{5}{15}}$ Bring the whole numbers together and the fractions together: $= {9} + {12} + {\dfrac{1}{10}} + {\dfrac{5}{15}}$ Add the whole numbers: $=21 + {\dfrac{1}{10}} + {\dfrac{5}{15}}$ Simplify each fraction: $= 21 + {\dfrac{1}{10}} + {\dfrac{1}{3}}$ Find a common denominator for the fractions: $= 21+\dfrac{3}{30}+\dfrac{10}{30}$ Add the fractions: $= 21+\dfrac{13}{30}$ Combine the whole and fractional parts into a mixed number: $= 21\dfrac{13}{30}$